ALGEBRA 1 LESSON 6 3 Standard Form Examples

ALGEBRA 1 LESSON 6 -3 Standard Form ) Examples 3 x + y = 5 -2 x + y = 10 x – y = 6 20 x + 4 y = 8 9 x - 3 y = 1 2 x + 5 y = 4 8 -5

ALGEBRA 1 LESSON 6 -3 Standard Form Find the x- and y-intercepts of 2 x + 5 y = 6. Step 1 To find the x-intercept, substitute 0 for y and solve for x. 2 x + 5 y = 6 Step 2 To find the y-intercept, substitute 0 for x and solve for y. 2 x + 5 y = 6 2 x + 5(0) = 6 2(0) + 5 y = 6 2 x = 6 x = 3 5 y = 6 6 y = 5 6 5 The x-intercept is 3. The y-intercept is . 8 -5

ALGEBRA 1 LESSON 6 -3 Standard Form Graph 3 x + 5 y = 15 using intercepts. Step 2 Plot (5, 0) and (0, 3). Step 1 Find the intercepts. Draw a line through the points. 3 x + 5 y = 15 3 x + 5(0) = 15 3 x = 15 Substitute 0 for y. Solve for x. x = 5 3 x + 5 y = 15 3(0) + 5 y = 15 Substitute 0 for x. Solve for y. y = 3 8 -5

ALGEBRA 1 LESSON 6 -3 Standard Form a. Graph y = 4 b. Graph x = – 3. 0 • x + 1 • y = 4 Write in standard form. For all values of x, y = 4. 1 • x + 0 • y = – 3 Write in standard form. For all values of y, x = – 3. 8 -5

ALGEBRA 1 LESSON 6 -3 Standard Form 2 3 Write y = x + 6 in standard form using integers. 2 y = x + 6 3 2 3 y = 3( x + 6 ) Multiply each side by 3. 3 y = 2 x + 18 Use the Distributive Property. 3 – 2 x + 3 y = 18 Subtract 2 x from each side. The equation in standard form is – 2 x + 3 y = 18. 8 -5

ALGEBRA 1 LESSON 6 -3 Standard Form Write an equation in standard form to find the number of hours you would need to work at each job to make a total of $130. Job Mowing lawns Delivering newspapers Amount Paid per hour x Define: Let = the hours mowing lawns. y Let = the hours delivering newspapers. $12 $5 Relate: $12 per h plus mowing Write: $5 per h equals $130 delivering x + 5 y 12 = 130 The equation standard form is 12 x + 5 y = 130. 8 -5

ALGEBRA 1 LESSON 6 -3 Standard Form Find each x- and y-intercepts of each equation. 1. 3 x + y = 12 2. – 4 x – 3 y = 9 9 x = – , y = – 3 x = 4, y = 12 4 3. Graph 2 x – y = 6 using x- and y-intercepts. For each equation, tell whether its graph is horizontal or vertical. 4. y = 3 horizontal 5. x = – 8 vertical 5 6. Write y = x – 3 in standard form using integers. 2 – 5 x + 2 y = – 6 or 5 x – 2 y = 6 8 -5